FOR MANY years, Martin Gardner has delighted read ers of Scientific
American with his column of mathematical puzzles and brainteasers. If you
want to escape from the tedium of Christmas afternoon television, take a
dip into Gardner’s collected works, which are on offer as three volumes
in a gift box. They provide a splendid melange of intriguing puzzles, illuminating
insights into the workings of the mathematical mind and entertaining anecdotes
about the games that mathematicians can play.

Take for instance, the geometrical Chinese puzzles called tangrams.
They are attributed to Tan, the legendary Chinese writer who lived 4000
years ago. Well, not really. The historyof the tangram, Gardner tellsus,
was a hoax invented at theturn of the century. Nevertheless, the myth found
its way into encylopaedias and scholarly works.

Gardner also describes how another kind of Chinese puzzle – the mechanical
kind that is composed of interlocking pieces – has been transformed into
high art. The Spanish sculptor Miguel Berrocal studied both mathematics
and architecture. His truly fantastic creations of heads and torsos are
made up of intricately interlocking pieces of metal, which can be taken
apart only by removing one piece at a time in the correct order. To the
right is one of Berrocal’s most humorous and complicated works, the torso
of Goliath, which contains 80 pieces. Apparently, the fig leaf can be rotated
to expose the genitals, of which there are alternative designs, one circumcised
and one not.